Period-doubling cascades of a Silnikov equation

TL;DR

This paper investigates three distinct period-doubling cascades in a Silnikov equation, utilizing numerical methods and the Feigenbaum constant to estimate bifurcation points, and introduces concepts like separator and pseudo-attractor.

Contribution

It presents a detailed numerical analysis of multiple period-doubling cascades in a Silnikov system, incorporating Feigenbaum's constant for bifurcation estimation and introducing new theoretical concepts.

Findings

Identified three different period-doubling cascades.

Successfully estimated critical bifurcation parameters using Feigenbaum's constant.

Introduced the concepts of separator and pseudo-attractor in the context of Silnikov equations.

Abstract

Based on numerical results of a Silnikov equation, three period-doubling cascades, corresponding respectively to three different characters of the rotation number of a limit closed orbit, are studied, and the Feigenbaum constant is used successfully in the estimation of the critical parameter values for the period-doubling bifurcation. The conceptions of separaror and pseudo-attractor are also introduced in the discussion part of this paper.